Difference Between Centre of Mass and Centre of Gravity

Whether it makes a difference or not all depends
on size...

Now, as I mentioned in my previous post, the terms 'centre of mass' and 'centre of gravity' can be used almost interchangeably. However, this is only when we refer to relatively small objects, such as those which we find on the earth.
The difference between centre of mass and centre of gravity is fairly simple.
The centre of mass is a single point inside (or outside) any object where all of its mass effectively acts. In a regular 3D shape, such as a sphere, this would be the dead centre, however in a more complex shape it would be different.
The centre of gravity however, is where all gravity acts on an object. On earth the centre of mass is practically where all gravity acts so they can be used interchangeably. However, we know that gravitational pull depends on two things: distance between two objects and the mass of the object. The mass of the object will obviously always stay the same, however the distance from the object can change.
Consider an object as big as the moon. The distance from the earth on one side, would be much smaller than the opposite side. This means that since there is a substantial difference in pull between different parts of the 'object', the centre of gravity will be affected.
So there you go. There is always a difference between centre of mass and centre of gravity, but sometimes it is so minute that we consider it insignificant. This is due to the object being fairly small. However as the object gets larger, we begin to feel the need to distinguish between the two.
If you have any questions then, again, please feel free to leave them in the comments box below.